During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of about 165 km. How long did it take to go around the Moon once?

Answer 1

1) Find the radius of the moon. I will call it M.

2) Add the altitude above the moon's surface to the moon's radius. This will give you the radius of the command module's circular orbit (we are assuming the orbit is circular).
So you have r = M + 165km

3) Now find the circumference of the circle, or orbit. Use the equation C = 2(pi)r.

4) Now you know the distance for each orbit. Is that what the question means by "how long"? If so, you are done. If not, you have more to do, such as determining the speed the command module traveled.